On the Kuramoto-Sivashinsky equation in a disk
Tom 73 / 2000
Annales Polonici Mathematici 73 (2000), 227-256
DOI: 10.4064/ap-73-3-227-256
Streszczenie
We consider the first initial-boundary value problem for the 2-D Kuramoto-Sivashinsky equation in a unit disk with homogeneous boundary conditions, periodicity conditions in the angle, and small initial data. Apart from proving the existence and uniqueness of a global in time solution, we construct it in the form of a series in a small parameter present in the initial conditions. In the stable case we also obtain the uniform in space long-time asymptotic expansion of the constructed solution and its asymptotics with respect to the nonlinearity constant. The method can work for other dissipative parabolic equations with dispersion.
